An alternative specification of generalized linear mixed models

• Published in: Computational statistics & data analysis Vol. 54; no. 2; pp. 575 - 584
• Main Authors: Sartori, N., Severini, T.A., Marras, E.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-02-2010; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Exact sciences and technology; General topics; Linear inference, regression; Mathematics; Multivariate analysis; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Sciences and techniques of general use; Statistics; Data analysis; Generalized linear model; Exponential distribution; Bias; Statistical estimation; Covariate; Random distribution; Independent variable; Linear model; Canonical form; Statistical regression; Statistical computation; Mixed model; Distribution function; Random effect; Exponential family; Random variable; Biased estimation
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2009.09.030

Consider stratified data in which
Y
i
1
,
…
,
Y
i
n
i
denote real-valued response variables corresponding to the observations from stratum
i
,
i
=
1
,
…
,
m
and suppose that
Y
i
j
follows an exponential family distribution with canonical parameter of the form
θ
i
j
=
x
i
j
β
+
γ
i
. In analyzing data of this type, the stratum-specific parameters are often modeled as random effects; a commonly-used approach is to assume that
γ
1
,
…
,
γ
m
are independent, identically distributed random variables.
The purpose of this paper is to consider an alternative approach to defining the random effects, in which the stratum means of the response variable are assumed to be independent and identically distributed, with a distribution not depending on
β
. It will be shown that inferences about
β
based on this formulation of the generalized linear mixed model have many desirable properties. For instance, inferences regarding
β
are less sensitive to the choice of random effects distribution, are less subject to bias from omitted stratum-level covariates and are less affected by separate between- and within-cluster covariate effects.